Truth tables for conditional propositions.

Question

I’m taking discrete math and I’m already completely lost on how to make truth tables for conditional propositions such as q → ¬(r ∨ q) .

In: 2

Answer 1

Take your proposition and make a column for every variable and every operation.

Then create a number rows equal to 2^n where n is the number of variables. This allows you to exercise every possible combination. For example, with 3 variables you have FFF, FFT, FTF, FTT, TFF, TFT, TTF, TTT. Note: These are the same as counting from 0 to 2^n – 1 in binary.

Then you simply calculate the results for each combination using the order of operations (negation first, then and, then or, then implication). Parentheses work in the same way they do with conventional arithmetic.

So in your above equation, you’d create the column for v with the variables r and q. Then you’d create the column for – with the column for v. Finally, you’d create the column for implication with q and the column for -.